Respuesta :
Perpendicular bisector passes through midpoint of the line joining the given two points so the equation for this perpendicular bisector of the line segment whose endpoint are (7,-1) and (-9,-5) is 4x-y=29.
What is a bisector of a line?
To divide a segment or an angle into two congruent sections is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.
Is a bisector always a straight line?
A straight line called a bisector divides an angle or a line into two equal pieces. The bisector of a segment always travels through the middle of the segment.
For this problem you have to find the mid point of the line joining
the given points and also the slope of the perpendicular line.
Here, A(7,-1) and B(-9,-5) are the given two points.
let
C is the mid point and CD is the perpendicular through C
Midpoint of AB=[x1+x2)/2,(y1+y2)/2]
C=((7-9)/2,(-1-5)/2)
C=(-1,-3)
Slope of AB=(y2−y1)/(x2−x1)
=(-5+1)/(-9-7)
=4/16
=1/4
Slope of CD=4
Equation of line;
(y−y1)=m(x−x1)
(y+1)=4(x−7)
Y+1=4x-28
4x-y=29
this is our required solution.
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